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Video "Finite fields made easy by Randell Heyman (2015)" at youtu.be/z9bTzjy4SCg?t=159 shows how for order . Basically, for order , we take:For a worked out example, see: GF(4).
- each element is a polynomial in , , the polynomial ring over the finite field with degree smaller than . We've just seen how to construct for prime above, so we're good there.
- addition works element-wise modulo on
- multiplication is done modulo an irreducible polynomial of order
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